60.1.452 problem 455

Internal problem ID [10466]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 455
Date solved : Monday, January 27, 2025 at 07:49:11 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a&=0 \end{align*}

✓ Solution by Maple

Time used: 0.190 (sec). Leaf size: 66

dsolve(x^3*diff(y(x),x)^2+x^2*y(x)*diff(y(x),x)+a = 0,y(x), singsol=all)
 

\begin{align*} y &= -\frac {2 \sqrt {a x}}{x} \\ y &= \frac {2 \sqrt {a x}}{x} \\ y &= \frac {c_{1}^{2} x +4 a}{2 x c_{1}} \\ y &= \frac {4 a x +c_{1}^{2}}{2 x c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.605 (sec). Leaf size: 57

DSolve[a + x^2*y[x]*D[y[x],x] + x^3*D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {e^{-\frac {c_1}{2}} \left (x+4 a e^{c_1}\right )}{2 x} \\ y(x)\to \frac {e^{-\frac {c_1}{2}} \left (x+4 a e^{c_1}\right )}{2 x} \\ \end{align*}